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Addendum to ``Dense subsets of the boundary of a Coxeter system''
Author(s):
Tetsuya
Hosaka
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3745-3747.
MSC (2000):
Primary 57M07, 20F65, 20F55
Posted:
July 7, 2005
Original article:
Proc. Amer. Math. Soc. 132 (2004), 3441-3448.
MathSciNet review:
2163614
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Abstract:
In this paper, we investigate boundaries of parabolic subgroups of Coxeter groups. Let  be a Coxeter system and let  be a subset of  such that the parabolic subgroup  is infinite. Then we show that if a certain set is quasi-dense in  , then  is dense in the boundary  of the Coxeter system  , where  is the boundary of  .
References:
-
- 1.
- M. R. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Springer-Verlag, Berlin, 1999. MR 1744486 (2000k:53038)
- 2.
- M. W. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983), 293-324. MR 0690848 (86d:57025)
- 3.
- -, Nonpositive curvature and reflection groups, in Handbook of Geometric Topology (Edited by R. J. Daverman and R. B. Sher), pp. 373-422, North-Holland, Amsterdam, 2002. MR 1886674 (2002m:53061)
- 4.
- -, The cohomology of a Coxeter group with group ring coefficients, Duke Math. J. 91 (no.2) (1998), 297-314. MR 1600586 (99b:20067)
- 5.
- T. Hosaka, Parabolic subgroups of finite index in Coxeter groups, J. Pure Appl. Algebra 169 (2002), 215-227. MR 1897344 (2003c:20041)
- 6.
- -, Dense subsets of the boundary of a Coxeter system, Proc. Amer. Math. Soc. 132 (2004), 3441-3448. MR 2073322
- 7.
- G. Moussong, Hyperbolic Coxeter groups, Ph.D. thesis, The Ohio State University, 1988.
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Additional Information:
Tetsuya
Hosaka
Affiliation:
Department of Mathematics, Utsunomiya University, Utsunomiya, 321-8505, Japan
Email:
hosaka@cc.utsunomiya-u.ac.jp
DOI:
10.1090/S0002-9939-05-08307-3
PII:
S 0002-9939(05)08307-3
Keywords:
Boundaries of Coxeter groups
Received by editor(s):
July 5, 2004
Received by editor(s) in revised form:
September 12, 2004 and October 5, 2004
Posted:
July 7, 2005
Additional Notes:
The author was partly supported by the Grant-in-Aid for Scientific Research, The Ministry of Education, Culture, Sports, Science and Technology, Japan (No.~15740029).
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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